**Decreasing Monster Hit-points & Increasing Monster Damage Proportionately**

I'm sure plenty of DMs have aimed for this goal: decreasing monster hit-points, and increasing their damage.

Decreasing the hit-points so combat goes faster, but increasing their damage so the monster remains as effective/challenging as it was with's full alotment of hit-points.

My question is: Is there a formula of some kind to decide how much damage should go up with respect to how much hit-points you remove?

My instinct tells me to keep the ratio linear. Example, if the monster is decreased 25% hit-points, increase the damage it deals by 25%. But I'm not sure if this is right, so I figure it'd ask. After all, if a monster deals 2d8+10, and I decrease him down to 1 hit-point, increasing his one attack to 4d8+20 (+100%) doesn't seem appropriate, since he'll go down in one hit... so is there a forumla for this?

Thanks!